High Nitrogen, Multi-Principal Element, High Entropy Corrosion Resistant Alloy

ABSTRACT

A multi-principal element, corrosion resistant alloy is disclosed. The alloy has the following composition in weight percent:
         Co about 13 to about 28   Ni about 13 to about 28   Fe+Mn about 13 to about 28   Cr about 13 to about 37   Mo about 8 to about 28   N about 0.10 to about 1.00.
 
The alloy also includes the usual impurities found in corrosion resistant alloys intended for the same or similar use. In addition, one or both of W and V may be substituted for some or all of the Mo. The alloy provides a solid solution that is substantially all FCC phase, but may include minor amounts of secondary phases that do not adversely affect the corrosion resistance and mechanical properties provided by the alloy.

CROSS REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application No. 62/468,600, filed Mar. 8, 2017, the entirety of which is incorporated herein by reference.

BACKGROUND OF THE INVENTION Field of the Invention

This invention relates to corrosion resistant austenitic steel alloys and in particular, to a multi-principal element, high entropy, corrosion resistant alloy that includes nitrogen.

Description of the Related Art

It is known that alloying elements such as chromium (Cr), molybdenum (Mo), and nitrogen (N) improve corrosion resistance of steel alloys, particularly resistance to localized attack in chloride containing environments. The degree of corrosion resistance can be predicted by a pitting resistance equivalent number (PREN). A known equation for determining the PREN of an alloy is PREN=Cr (wt. %)+3.3×Mo (wt. %)+16×N (wt. %). Other elements, such as tungsten, copper, and vanadium have been proposed as beneficial alloying additions for corrosion resistance. Cr and Mo are strong ferrite formers and can lead to the formation of sigma phase and chi phase which adversely affect both pitting resistance and mechanical properties. To offset the adverse effects of using higher amounts of Cr and Mo, austenite formers such as nickel, cobalt, and copper may be added to the alloys. This practice has led to the use of nickel-base and cobalt-base alloys for the most severely corrosive environments. The addition of N is known to be generally beneficial to both corrosion resistance and strength, but nitrogen solubility and the unwanted precipitation of nitrides, especially at grain boundaries, limits the total amount of nitrogen that can be added. Nitrogen solubility becomes increasingly limited as nickel and cobalt contents increase.

Among the known austenitic, corrosion resistance alloys, there are nickel-base and cobalt-base alloys that include significant amounts of Mo. In those alloys, a high Mo content is stabilized by either a high nickel content or a high cobalt content. Most of those alloys do not contain a positive addition of N. Alloy N-155 which is sold under the registered trademark MULTIMET® has the following nominal composition in weight percent: 20% Ni, 20% Co, 20% Cr, 3% Mo, 2.5% W, 1.5% Mn, 1% Nb+Ta, 0.15% N, and 0.1% C. The balance of the alloy is iron and usual impurities. Those alloys have essentially a single base element such as iron, nickel, or cobalt.

Alloy design has traditionally not considered the contributions of the mixing entropy to alloy phase stability because the mixing entropy is relatively low in systems with a single base element. Because they do not have a single base element, high entropy alloys (HEA) employ configurational entropy to affect the stability of solid structural phases within the alloy. By definition, HEA are composed of a single solid solution phase or a mixture of solid solution phases. With the exception of a few studies, the solid solution phases have either a body centered cubic (BCC) or a face centered cubic (FCC) structure. HEA typically consist of at least three elements in equiatomic or close to equiatomic proportions to maximize the configurational entropy. According to Guo et al., “Phase stability in high entropy alloys: Formation of solid-solution phase or amorphous phase”, Progress in Natural Science: Materials International, vol. 21, pp. 433-446 (2011), (the entirety of which is incorporated herein by reference) an alloy that meets the following rules regarding mixing enthalpy (ΔH_(mix)), mixing entropy (ΔS_(mix)), and atomic size difference (6) is more likely to provide a solid solution structure.

−22≤ΔH _(mix)≤7 kJ/mol

δ<8.5%

ΔS _(mix)≥11 J/(K mol)

The parameters ΔH_(mix), 6, and ΔS_(mix) are known and are defined in the technical literature. See, for example, Guo et al. at p. 434. The above-stated rules are based on experimental results from various published studies, but should be considered as broad guidelines.

The basic principles derived from the above-listed rules overlap with the Hume-Rothery rules relating to solid solution formation in alloys and are suitable starting point for designing an alloy with a solid solution structure. The mixing enthalpy should not be too negative or too positive in order to avoid the formation of intermetallic phases and to avoid phase separation. The atomic size difference between the constituent elements should be minimized to prevent lattice strain. Further, the mixing entropy should be maximized.

The electronegativity of the constituent elements should be similar among the principal elements. The solid solution phase that forms is also related to the valence electron concentration (VEC). Guo et al. also discloses that a single-phase FCC structure is predicted when VEC is greater than about 8, a single-phase BCC structure is predicted when the VEC is less than about 6.87, and a mixed FCC/BCC structure is predicted when 6.87<VEC<8.

SUMMARY OF THE INVENTION

In accordance with a first aspect of the present invention there is provided a multi-principal element, corrosion resistant alloy having the following composition in weight percent:

Co about 13 to about 28 Ni about 13 to about 28 Fe + Mn about 13 to about 28 Cr about 13 to about 37 Mo about 8 to about 28 N about 0.10 to about 1.00. The alloy also includes the usual impurities found in corrosion resistant alloys intended for the same or similar use. In addition, one or both of W and V may be substituted for some or all of the Mo. The alloy provides a solid solution that is substantially all FCC phase, but may include minor amounts of secondary phases that do not adversely affect the corrosion resistance and mechanical properties provided by the alloy.

In accordance with another aspect of the present invention there is provided a multi-element, corrosion resistant, high entropy alloy having the atomic formula (Fe, Mn)_(a)Co_(b)Ni_(c)Cr_(x)(Mo, W, V)_(y) wherein a and b are each 12-35 atomic percent (at. %), c and x are each 12-40 at. %, and y is 4-20 at. %. W and/or V may be substituted for some or all of the Mo on an equiatomic basis. The alloy also comprises from at least about 0.10% N up to the solubility limit.

Within the foregoing alloy compositions, the elements are selected to provide the following combination of parameters;

−6 kJ/mol<ΔH _(mix)≤0 kJ/mol;

2.00%<δ<4.5%;

ΔS _(mix)>12 J/K mol; and

the valence electron concentration is greater than about 7.80.

It is contemplated that the alloy according to the present invention may comprise or may consist essentially of the elements described above, throughout the following specification, and in the appended claims. Here and throughout this application the term “percent” and the symbol “%” mean percent by weight or percent by mass, unless otherwise indicated.

BRIEF DESCRIPTION OF THE DRAWING

The drawing is a graph of Rockwell C hardness (HRC) as a function of cold working percent for Example 5 of the alloy according to this invention.

DETAILED DESCRIPTION

By using the foregoing parameters in the design of multi-element alloy, corrosion resistant alloy, it is believed that higher amounts of elements such as molybdenum, tungsten, and vanadium, can be included in a CoCrNiMnFe base alloy to provide an FCC solid solution structure that is substantially free of undesired secondary phases. The alloy also includes a small amount of N as an interstitial element. An equiatomic or near-equiatomic composition comprising a combination of Cr, Mn, Fe, Co, and Ni provides the multi-element base of the high entropy alloy according to this invention. The combination of base elements is chosen because it meets the constraints for HEA outlined about. Interstitial elements such as N have not been studied extensively within the HEA design constructs and may require novel design considerations that go beyond the rules discussed above. Specifically, the use of ΔH_(mix) as an average term should be avoided in order to properly design an alloy in which nitride formation does not occur. Relatively large additions of Mo, W, or V in conjunction with N at or close to its solubility limit provides a novel alloy system with potentially superior corrosion resistance compared to the known Fe-base, Ni-base, and Co-base stainless steel alloys.

Nickel and cobalt are present in the high entropy alloy of this invention to help stabilize the preferred FCC phase. Nickel and cobalt also benefit the desired single phase nature of the alloy by reducing the precipitation of undesirable ordered phases such as sigma (σ) and mu (μ) phases in the solid solution. In this way nickel and cobalt benefit the ductility provided by the alloy. Nickel and cobalt are relatively expensive elements and so their contents are limited to control the cost of making the alloy of this invention.

Chromium contributes to the general and localized corrosion resistance provided by this alloy. It is also believed that chromium helps to increase the solubility of nitrogen in the alloy. Too much chromium adversely affects the mechanical properties (e.g., ductility) and corrosion resistance by promoting the precipitation of ordered phases, like sigma and/or Chromium nitrides.

The alloy also contains about 4 to about 20 atomic percent (at. %) or at least about 8% up to about 28% weight percent of molybdenum to benefit the alloy's resistance to localized corrosion such as pitting corrosion. Too much molybdenum promotes the precipitation and stabilization of topologically close packed phases which adversely affects the corrosion resistance and mechanical properties. Like chromium too much molybdenum adversely affects the ductility and processability of the alloy because it forms sigma phase at relatively high temperatures. Tungsten and/or vanadium can be substituted for some or all of the molybdenum on an equiatomic basis.

Manganese is present in the alloy of this invention because it benefits the solubility of nitrogen in the solid solution of the alloy. Too much manganese reduces the solidus temperature of the alloy which can adversely affect the intergranular strength during hot working.

Iron contributes to the high entropy of mixing (ΔS_(mix)) that characterizes this alloy and helps to stabilize the desired single phase FCC structure of the alloy. Iron is also present as a substitute for some of the nickel and/or cobalt to help limit the cost of producing the alloy. Similar to chromium and molybdenum, too much iron can result in the precipitation of sigma phase which adversely affects the ductility of the alloy and its processability.

At least about 0.10% nitrogen is also present in this alloy as an interstitial element. The addition of nitrogen helps to further stabilize the FCC phase and benefits the localized corrosion resistance provided by the alloy. As an interstitial element nitrogen also contributes to the good mechanical properties provided by the alloy such as its yield strength and tensile strength. Nitrogen may be present up to its solubility limit in the alloy, but preferably is limited to not more than about 1.00% in this alloy.

The alloy according to the present invention may also include copper to benefit the stability of the FCC phase structure. However, too much copper, reduces the solidus temperature of the alloy which can result in incipient intergranular liquation during hot working of the alloy.

An alloy in accordance with this invention provides very good resistance to corrosion, especially pitting corrosion. In this regard the alloy is characterized by having a pitting resistance equivalent number (PREN) of at least 50 where the PREN is defined as follows: PREN=% Cr+3.3×% Mo+16×% N. Preferably, the alloy is characterized by a PREN of at least about 65 and better yet at least about 70.

The elements that constitute the alloy of this invention are selected to provide the following combination of parameters;

−6 kJ/mol≤ΔH _(mix)≤0 kJ/mol;

2.00%<δ<4.5%;

ΔS _(mix)>12 J/K mol; and

the valence electron concentration (VEC) is greater than about 7.80. ΔS_(mix) is mainly affected by the number of main elements in the alloy and their concentrations. Preferably, a minimum of five equiatomic elements provide a ΔS_(mix) that results in a stabilized alloy microstructure. In the five-element embodiment of the alloy it is expected that ΔS_(mix) will be not more than about 13-13.5 J/K mol. However, in the copper-containing embodiment it is expected that ΔS_(mix) will be greater than 13-13.5 J/K mol. ΔH_(mix) is determined by the chemical affinity of the constituent elements and is preferably as close to zero as practicable to allow the entropy to manage the stability of the alloy. The parameter δ is related to the difference in atomic size of the constituent elements. In this alloy, molybdenum is the largest atom and is the one that most affects the value of δ.

Valence electron concentration is the number of total electrons in the valence band including the “d” electrons. Cobalt and nickel have the higher VEC's, 9 and 10 respectively, than the other elements. However, since this is an alloy, the VEC is calculated as

VEC=Σ_(i) ^(n) Ci(VEC)i

Where C_(i) is the concentration of element i. Co and Ni affect the VEC in this alloy. Preferably, the alloy according to this invention provides a VEC greater than 8.0.

Working Examples

In order to demonstrate the properties provided by the alloys according to this invention six heats were vacuum induction melted and then cast as 40-lb. ingots. The weight percent compositions of the six heats are set forth in Table 1 below as Examples 1-6.

TABLE 1 Ex. 1 Ex. 2 Ex. 3 Ex. 4 Ex. 5 Ex. 6 N 0.137 0.229 0.130 0.167 0.227 0.128 Si 0.03 0.03 0.02 0.03 0.03 0.03 Cr 13.30 20.25 13.30 15.77 21.94 13.50 Ni 21.60 17.44 33.50 32.68 27.70 22.44 Mo 17.25 12.84 17.71 16.20 12.72 17.48 Co 26.45 25.40 17.27 16.93 19.84 25.81 Fe + Mn 21.23 23.81 18.07 18.22 17.54 20.61

After solidification it was determined that the ingots contained mainly a solid solution consisting essentially of an FCC structure with some interdendritic secondary phase(s). The 40-lb ingots were homogenized, forged to 0.75″ square bars, and then solution annealed at 2250 F for 2.5 hrs. followed by water quenching. It was determined that the alloy had a solid solution structure consisting substantially of the FCC phase in the solution-annealed-and-quenched condition.

Test specimens for critical pitting temperature testing, potentiodynamic testing, and slow strain rate testing were obtained from the solution annealed 0.75″ square bars prepared from each ingot. Critical pitting temperature (CPT) testing was performed in a 1 M solution of NaCl at 0.7 volts with a nitrogen gas purge in accordance with ASTM Standard Test Procedure G150. The results of the CPT testing are shown in Table 2 below.

TABLE 2 CPT Ex. 1 >99.7° C. Ex. 2 90.65° C. Ex. 3 >95° C. Ex. 4 >95° C. Ex. 5 >95° C. Ex. 6 >95° C.

Cyclic polarization potentiodynamic testing was performed based on ASTM Standard Test Procedure G61. Voltage values at the knee of the curve, at 50 μA/cm², and at 100 μA/cm² were measured for two sets of samples prepared from solution annealed 0.75″ square bars. The results of the potentiodynamic pitting tests are shown in Table 3 below including the pitting potentials and the repassivation potentials in millivolts (mV).

TABLE 3 Pitting Pitting Pitting Potential Potential Potential Repassivation @ Knee @ 50 μA/cm2 @ 100 μA/cm2 Potential Ex. 1 891.5 949.3 961.9 846.3 Ex. 2 887.2 946.4 956.3 784.2 Ex. 3 937.9 966.1 974.6 853.3 Ex. 4 914.8 950.7 956.7 858 Ex. 5 921.3 961.2 965.8 867 Ex. 6 943.2 967.2 973.1 849

Another set of samples were obtained from the 0.75 in. bars of each example for testing resistance to corrosion in acidic solutions. The samples were tested after immersion in a boiling aqueous solution containing 85% by volume of phosphoric acid (H₃PO₄). Additional samples were tested after immersion in a boiling aqueous solution containing 60% by volume of nitric acid (HNO₃). Further samples were tested after immersion in an of acid mixture in accordance ASTM Standard Test Procedure G28-02, Practice A. A fourth set of samples were tested after immersion in an of acid mixture in accordance ASTM Standard Test Procedure G28-02, Practice B. The results of the acidic corrosion tests for each example are presented in Table 4 including the weight loss in mills per year (mpy). Table 4 includes a qualitative assessment of the severity of intergranular attack for the specimens tested in accordance with ASTM G28-02, Methods A and B.

TABLE 4 Heat 85% 65% Sample H₃PO₄ HNO₃ ASTM G28-B ASTM G28-A Ex. 1 60.5 568.5 112.1 Light IGA 799.7 Severe IGA Ex. 2 609.9 96.7 5.8 NVA 712.6 Severe IGA Ex. 3 N/A* 904.5 N/A* N/A 480.4 Severe IGA Ex. 4 55.55 335.8 21.35 NVA 139.2 Light IGA Ex. 5 124 22.4 2 NVA 16.5 NVA Ex. 6 74.85 1125.7 81.95 Light IGA 471.4 Severe IGA IGA = Intergranular attack. NVA = Nonvisible attack *The test could not be completed because of technical difficulties and insufficient material for retesting.

The data presented in Tables 2, 3, and 4 show that all the examples provided very good resistance to pitting in a chloride-containing environment, as well as good resistance to intergranular corrosion in acidic environments.

Slow strain rate testing of specimens from Examples 1, 2, 4, and 5 was performed in each of three different environments: ambient air, a 3.5% NaCl solution at boiling temperature, and a 3.5% NaCl solution at boiling temperature with a pH of 1.0. The results of the slow strain rate testing are shown in Table 5 below including the percent elongation (% El.), the percent reduction in area (% RA), and the number of hours to fracture (Hours). Also shown in Table 5 are the results of each tested property presented as a percentage of the same property measured in air. In the last column of Table 5 is shown the “% of Air—Composite” which is the average of the % El. Air Avg, % RA Air Avg, and Hr Air Avg. It is calculated as (% El. Air Avg.+% RA Air Avg.+Hrs. Air Avg.)/3.

TABLE 5 % El. % RA as % as % Hrs. as of of % of Air Air Air % of Air Environment % El. Avg. % RA Avg. Hours Avg. Composite Ex. 1 Air 92.8 — 75.0 — 59.1 — — 3.5 NaCl @ 92.6 99.8 73.0 97.3 46.4 78.5 91.9 Boiling 3.5 NaCl @ 88.6 95.4 73.0 97.3 42.9 72.6 88.4 Boiling, pH 1.0 Ex. 2 Air 91.1 — 72.8 — 45.5 — — 3.5 NaCl @ 92.0 100 65.9 90.5 41.5 91.2 93.9 Boiling 3.5 NaCl @ 87.9 96.5 65.0 89.3 42.5 93.4 93.1 Boiling, pH 1.0 Ex. 4 Air 87.7 74.8 61.5 3.5 NaCl @ 87.2 99.43 75 100 60.3 98.05 99.1 Boiling 3.5 NaCl @ 81.4 92.82 70 93.58 54.1 87.97 91.4 Boiling, pH 1.0 Ex. 5 Air 90.7 79.5 63.1 3.5 NaCl @ 87.1 96.03 70.2 88.30 60.2 95.4 93.2 Boiling 3.5 NaCl @ 73.7 81.26 54.3 68.30 50.7 80.35 76.6 Boiling, pH 1.0

The results presented in Table 5 show that Examples 1, 2, 4, and 5 are practically immune to boiling 3.5% NaCl, even at a pH of 1.0, thereby showing the good corrosion resistance in the boiling sodium chloride environment.

Two sets of longitudinal tensile samples were prepared from the bars of Examples 4, 5, and 6, one set for mechanical testing at room temperature (25° C.) and the other set for testing at a cryogenic temperature (−100° C.). The results of the room temperature tensile testing are presented in Table 6 and the results of the cryogenic tensile testing are presented in Table 7. For both sets of tests the results include the 0.2% offset yield strength (Y.S) and the ultimate tensile strength (U.T.S.) in ksi (MPa), the percent elongation in 4 diameters (% El.), and the percent reduction in area (% R.A.).

TABLE 6 Y.S. U.T.S. Ex. ksi MPa ksi MPa % El. % R.A. 4 51.3 354 111 765 73 29 5 55.9 385 118 813 72 29 6 54.4 375 112 772 70 26

TABLE 7 Y.S. U.T.S. Ex. ksi MPa ksi MPa % El. % R.A. 4 72.8 502 138 951 78 26 5 77.2 532 148 1020 76 27 6 74.6 514 139 958 87 23

One of the important properties in this alloy is the very high ductility provided by the alloy as demonstrated by the high elongation values set forth in Tables 6 and 7. By way of example, the percent elongation provided by the alloy is up to 73% at room temperature which compares very favorably to 58% elongation provided by the known stainless steels. However, more important is the capability to provide that level of ductility even at cryogenic temperatures without adversely affecting the tensile strength provided by the alloy as shown in Table 7.

In addition to the exceptional corrosion resistance and mechanical properties provided by the alloy according to the invention as presented in Tables 2 through 7, this alloy provides excellent cold processability as demonstrated by its cold work hardening capability. In this regard, the alloy is able to provide a Rockwell C-scale hardness (HRC) of about 37 after about 30% cold work, where the percent cold work is defined by the equation below:

${\% \mspace{14mu} {CW}} = \frac{{{Initial}\mspace{14mu} {Area}} - {{final}\mspace{14mu} {Area}}}{{Initial}\mspace{14mu} {Area}}$

In order to demonstrate the good cold processability provided by this alloy, material from Example 5 was cold worked to increasing percent reductions in cross-sectional area and the HRC was measured at several intervals. The results are shown is shown the drawing FIGURE as a graph of the measured HRC values as a function of the percent cold reduction. The graphed data shows the unexpectedly high ductility provided by this alloy allows the alloy to be cold worked up to 70% or more while reaching a hardness of about 45 HRC.

The terms and expressions which are employed in this specification are used as terms of description and not of limitation. There is no intention in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof. It is recognized that various modifications are possible within the invention described and claimed herein. 

1. A multi-principal element, high entropy, corrosion resistant alloy having a solid solution phase and wherein the alloy comprises, in weight percent: Co about 13 to about 28 Ni about 13 to about 35 Fe + Mn about 13 to about 28 Cr about 13 to about 37 Mo about 8 to about 28 N about 0.10 to about 1.00

and the usual impurities, wherein one or both of W and V may be substituted for some or all of the Mo.
 2. The multi-principal element, corrosion resistant alloy claimed in claim 1 wherein the solid solution phase consists essentially of a face-centered-cubic crystalline structure.
 3. The multi-principal element, corrosion resistant alloy claimed in claim 1 wherein the alloy has the following characteristics: −6 kJ/mol<ΔH _(mix)<0 kJ/mol, ΔS _(mix)>12 J/(K mol), 2.00%<δ<4.5%, and the valence electron concentration of the alloy is greater than about 7.80.
 4. A high entropy, corrosion resistant alloy that forms a single phase solid solution, said alloy having the formula (Fe, Mn)_(a)Co_(b)Ni_(c)Cr_(x)(Mo, W, V)_(y) wherein a, b, c, x, and y are as follows in atomic percent, 12≤a≤35, 12≤b≤35, 12≤c≤40, 12≤x≤40, 4≤y≤20, wherein W and V may be substituted for some or all of Mo on an equiatomic basis, and wherein the alloy comprises from at least about 0.10% N up to the solubility limit.
 5. The high entropy, corrosion resistant alloy claimed in claim 4 wherein the solid solution phase consists essentially of a face centered cubic crystalline structure.
 6. The high entropy, corrosion resistant alloy claimed in claim 4 wherein the alloy has the following characteristics: −6 kJ/mol≤ΔH _(mix)≤0 kJ/mol, ΔS _(mix)>12 J/(K mol), 2.00%<δ<4.5%, and the valence electron concentration of the alloying elements is greater than about 7.80.
 7. A high entropy, corrosion resistant alloy having a solid solution phase and wherein the alloy comprises, in weight percent: Co about 13 to about 28 Ni about 13 to about 35 Cu about 13 to about 28 Fe + Mn about 13 to about 28 Cr about 13 to about 37 Mo about 8 to about 28 N about 0.10 to about 1.00

and the usual impurities, wherein one or both of W and V may be substituted for some or all of the Mo.
 8. The high entropy, corrosion resistant alloy claimed in claim 7 wherein the solid solution phase consists essentially of a face centered cubic crystalline structure.
 9. The high entropy, corrosion resistant alloy claimed in claim 7 wherein the alloy has the following characteristics: −6 kJ/mol<ΔH _(mix)≤0 kJ/mol, ΔS _(mix)>12 J/(K mol), 2.00%<δ<4.5%, and the valence electron concentration of the alloy is greater than about 7.80.
 10. A high entropy, corrosion resistant alloy that forms a single phase solid solution, said alloy having the formula (Fe, Mn)_(a)Co_(b)Ni_(c)Cu_(d)Cr_(x)(Mo, W, V)_(y) wherein a, b, c, x, and y are as follows, in atomic percent, 10≤a≤30, 10≤b≤30, 10≤c≤30, 10≤d≤30 10≤x≤30, 4≤y≤18, wherein W and V may be substituted for some or all of Mo on an equiatomic basis, and wherein the alloy comprises from at least about 0.10% N up to the solubility limit.
 11. The high entropy, corrosion resistant alloy claimed in claim 10 wherein the solid solution phase consists essentially of a face centered cubic crystalline structure.
 12. The high entropy, corrosion resistant alloy claimed in claim 10 wherein the alloy has the following characteristics: −6 kJ/mol≤ΔH _(mix)≤0 kJ/mol, ΔS _(mix)>12 J/(K mol), 2.00%<δ<4.5%, and the valence electron concentration of the alloying elements is greater than about 7.80. 